SOFIANE Boufal struck late to condemn Albion to defeat in terrible conditions at Southampton on Saturday evening.
The Baggies, having drawn 1-1 away at Leicester on Monday night, looked to have held out for a battling 0-0 at a wet and windy St Mary's Stadium.
But Boufal's stunning solo effort five minutes from time gave the hosts all three points on the south coast.
Ryan Bertrand went close when his deflected free-kick hit the angle while fit-again Ben Foster produced impressive saves to deny Saints pair Dusan Tadic and Maya Yoshida.
Nacer Chadli forced a fingertip save from Fraser Forster while Jay Rodriguez could not take advantage of a second-half opening against his former club.
Albion will be concerned by a first-half injury to captain Jonny Evans, who was forced to hobble off.
Having missed out against the Foxes with a knee complaint, Foster returned between the sticks for Albion, who threatened early on as Gareth Barry's long-range strike rippled the side-netting.
Saints went closer after 17 minutes when Bertrand's free-kick was bravely deflected on to the upright by the head of a leaping Evans in the wall.
Tadic tested Foster before Oriol Romeu hooked wide from two yards at a corner and Shane Long poked narrowly off target on the counter-attack.
Albion lost skipper Evans to injury midway through the a first half in which Yoshida twice threatened just before half-time, Foster producing a smart reflex save before an acrobatic effort flew off target.
Gareth McAuley replaced Barry shortly after the interval, with the Baggies switching system to three at the back.
And they immediately put pressure on Saints, Rodriguez dragging a clear opening wide having been sent through by Grzegorz Krychowiak.
Foster produced a superb block to keep out Tadic, who then saw penalty appeals waved away for an alleged pull by the Baggies No.1.
Chadli forced a fingertip save from Forster as both goalkeepers had the best of the action.
But it was Boufal who brought the match-winning moment in the 85th minute. The Moroccan picked the ball up in his own half, skipped past four Baggies defenders and lashed past Foster.
Albion pressed but were unable to find an equaliser.
ALBION: Foster, Dawson, Hegazi, Evans (Nyom 32), Gibbs, Barry (McAuley 53), Livermore, Krychowiak, Rodriguez, Chadli (Phillips 77), Rondon.
Subs: Myhill, Yacob, Brunt, McClean.